Characteristics optimization via compressed sensing in quantum state estimation

Compressed sensing (CS) has been proved efficiently in reducing the required number of measurements in the quantum state estimation. In this paper, the relationship between the optimal number of measurement settings and the error of quantum state estimation via compressed sensing are studied by means of analyzing the lower bound of measurement settings and upper bound of error of quantum state estimation. Based on the results obtained by the CS theory, we analyze the above mentioned characteristics of three observation matrices and give the performance comparisons through the numerical simulations. The obtained optimal conditions and error bounds in the state estimation process can provide theoretical instructions for the selection of the minimum number of measurement settings in the quantum state estimation.

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